zgetrf.f

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C> \brief \b ZGETRF VARIANT: left-looking Level 3 BLAS version of the algorithm.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZGETRF ( M, N, A, LDA, IPIV, INFO)
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, M, N
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX*16         A( LDA, * )
*       ..
*
*  Purpose
*  =======
*
C>\details \b Purpose:
C>\verbatim
C>
C> ZGETRF computes an LU factorization of a general M-by-N matrix A
C> using partial pivoting with row interchanges.
C>
C> The factorization has the form
C>    A = P * L * U
C> where P is a permutation matrix, L is lower triangular with unit
C> diagonal elements (lower trapezoidal if m > n), and U is upper
C> triangular (upper trapezoidal if m < n).
C>
C> This is the left-looking Level 3 BLAS version of the algorithm.
C>
C>\endverbatim
*
*  Arguments:
*  ==========
*
C> \param[in] M
C> \verbatim
C>          M is INTEGER
C>          The number of rows of the matrix A.  M >= 0.
C> \endverbatim
C>
C> \param[in] N
C> \verbatim
C>          N is INTEGER
C>          The number of columns of the matrix A.  N >= 0.
C> \endverbatim
C>
C> \param[in,out] A
C> \verbatim
C>          A is COMPLEX*16 array, dimension (LDA,N)
C>          On entry, the M-by-N matrix to be factored.
C>          On exit, the factors L and U from the factorization
C>          A = P*L*U; the unit diagonal elements of L are not stored.
C> \endverbatim
C>
C> \param[in] LDA
C> \verbatim
C>          LDA is INTEGER
C>          The leading dimension of the array A.  LDA >= max(1,M).
C> \endverbatim
C>
C> \param[out] IPIV
C> \verbatim
C>          IPIV is INTEGER array, dimension (min(M,N))
C>          The pivot indices; for 1 <= i <= min(M,N), row i of the
C>          matrix was interchanged with row IPIV(i).
C> \endverbatim
C>
C> \param[out] INFO
C> \verbatim
C>          INFO is INTEGER
C>          = 0:  successful exit
C>          < 0:  if INFO = -i, the i-th argument had an illegal value
C>          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
C>                has been completed, but the factor U is exactly
C>                singular, and division by zero will occur if it is used
C>                to solve a system of equations.
C> \endverbatim
C>
*
*  Authors:
*  ========
*
C> \author Univ. of Tennessee
C> \author Univ. of California Berkeley
C> \author Univ. of Colorado Denver
C> \author NAG Ltd.
*
C> \date December 2016
*
C> \ingroup variantsGEcomputational
*
*  =====================================================================
      SUBROUTINE zgetrf ( M, N, A, LDA, IPIV, INFO)
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         A( LDA, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE
      parameter( one = (1.0d+0, 0.0d+0) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, IINFO, J, JB, K, NB
*     ..
*     .. External Subroutines ..
      EXTERNAL           zgemm, zgetf2, zlaswp, ztrsm, xerbla
*     ..
*     .. External Functions ..
      INTEGER            ILAENV
      EXTERNAL           ilaenv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -4
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'zgetrf', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
.EQ..OR..EQ.      IF( M0  N0 )
     $   RETURN
*
*     Determine the block size for this environment.
*
      NB = ILAENV( 1, 'zgetrf', ' ', M, N, -1, -1 )
.LE..OR..GE.      IF( NB1  NBMIN( M, N ) ) THEN
*
*        Use unblocked code.
*
         CALL ZGETF2( M, N, A, LDA, IPIV, INFO )
 
      ELSE
*
*        Use blocked code.
*
         DO 20 J = 1, MIN( M, N ), NB
            JB = MIN( MIN( M, N )-J+1, NB )
*
*
*           Update before factoring the current panel
*
            DO 30 K = 1, J-NB, NB
*
*              Apply interchanges to rows K:K+NB-1.
*
               CALL ZLASWP( JB, A(1, J), LDA, K, K+NB-1, IPIV, 1 )
*
*              Compute block row of U.
*
               CALL ZTRSM( 'left', 'lower', 'no transpose', 'unit',
     $                    NB, JB, ONE, A( K, K ), LDA,
     $                    A( K, J ), LDA )
*
*              Update trailing submatrix.
*
               CALL ZGEMM( 'no transpose', 'no transpose',
     $                    M-K-NB+1, JB, NB, -ONE,
     $                    A( K+NB, K ), LDA, A( K, J ), LDA, ONE,
     $                    A( K+NB, J ), LDA )
   30       CONTINUE
*
*           Factor diagonal and subdiagonal blocks and test for exact
*           singularity.
*
            CALL ZGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
*
*           Adjust INFO and the pivot indices.
*
.EQ..AND..GT.            IF( INFO0  IINFO0 )
     $         INFO = IINFO + J - 1
            DO 10 I = J, MIN( M, J+JB-1 )
               IPIV( I ) = J - 1 + IPIV( I )
   10       CONTINUE
*
   20    CONTINUE
 
*
*        Apply interchanges to the left-overs
*
         DO 40 K = 1, MIN( M, N ), NB
            CALL ZLASWP( K-1, A( 1, 1 ), LDA, K,
     $                  MIN (K+NB-1, MIN ( M, N )), IPIV, 1 )
   40    CONTINUE
*
*        Apply update to the M+1:N columns when N > M
*
.GT.         IF ( NM ) THEN
 
            CALL ZLASWP( N-M, A(1, M+1), LDA, 1, M, IPIV, 1 )
 
            DO 50 K = 1, M, NB
 
               JB = MIN( M-K+1, NB )
*
               CALL ZTRSM( 'left', 'lower', 'no transpose', 'unit',
     $                    JB, N-M, ONE, A( K, K ), LDA,
     $                    A( K, M+1 ), LDA )
 
*
.LE.               IF ( K+NBM ) THEN
                    CALL ZGEMM( 'no transpose', 'no transpose',
     $                         M-K-NB+1, N-M, NB, -ONE,
     $                         A( K+NB, K ), LDA, A( K, M+1 ), LDA, ONE,
     $                        A( K+NB, M+1 ), LDA )
               END IF
   50       CONTINUE
         END IF
*
      END IF
      RETURN
*
*     End of ZGETRF
*
      END